The Physics of Music


Introduction


We hear music every day. The hottest songs on the radio, our private stash of favorites on our iPods, or even the choir or band geeks wailing away down the hallway. But what is it that goes behind that? Have you ever stopped to just consider what all is held in that single note you hear or tune you sing along with? The amount of complexity that goes into one single strand of musical notes would surprise you.


Anatomy of the Ear


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Image courtesy of Michael Rothschild, M.D. http://www.kids-ent.com/website/pediatric_ent/ear_infections/index.html
Starting with the basics, let’s cover the main thing that allows one to even hear music: the human ear. Hearing is one of the five senses that are learned in Kindergarten (hearing, sight, smell, touch and taste) that starts with your ears catching waves of sound . Sound waves are vibrations that objects produce that move through matter (be it a solid, such as a wall, a liquid, such as water, or a gas, such as the air) as sound. Teeny tiny variations in the matter surrounding you that create energy your ears pick up. It is the ear's job to take that energy and translate it into a form your brain can comprehend, nerve impulses that the brain perceives as sound. Auditory nerves found in the inner ear transmit these impulses from the waves the ear picks up to the temporal lobe of the cerebral cortex where they are recorded into the noises you hear everywhere, every day. So how do they get to those nerves? Well first they must be directed into the hearing section of your ear by the pinna, the outer part of your ear. The pinna is that funny-looking curved flap of cartilage that juts out from the side of your head, that part that you get pierced or use to tuck your hair behind. It’s the thing that most people think of when they hear the word ear. The pinnae are curved and face forward so as to be a "net" or a director of the sound waves that bounce against them. They are structured in that specific way so as to allow you to be able to determine what direction the sound is coming from. Each different way sound waves bounce off your ear produce a unique and specific pattern that your brain recognizes as forward, behind, above, or below, having a crucial part in a person's sense of direction. Since they face forward and are set flatly against the skull, it is easier for humans to hear what is in front of them than what is behind them. But you know how whenever you cup your ears with your hands, you can hear the sounds around you more sharply and effectively than you can whenever you just hear things with your ears alone? This is because your hands create a larger surface for sound waves to bounce off of and into your ears. So what exactly happens inside the ear when the sound waves make it in? Well, after the sound is directed through the ear canal, they reach the ear drum (the tympanic membrane) that is located between the ear canal and the middle ear. When the sound waves meet the ear drums, the drums are vibrated. One's ear drums are so sensitive that they pick up the smallest, slightest movement in air pressure. The vibrations pass through the middle ear to the inner ear where it is the job of the cochlea to translate them into the electric pulses that the brain can register as the distinct "sounds" that we hear.
[1] [2]


Patterns of Sound



Pitch/Frequency

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Cegep John Abbott College http://jac.michaeldrolet.net/physics/physics.htm

So what distinguishes the difference in sound waves and music waves? As mentioned above, sound waves are tiny vibrations that objects produce that move through matter and are caught by the ear to be translated into nerve impulses the brain recognizes as sound. So what makes a musical wave different from a normal sound wave? Well, since we know that a sound wave is produced when something vibrates, we must also understand that what we hear are the sound particles moving in a back and forth motion at a certain frequency. Referring to the frequency of a wave means how quickly the wave makes one back and forth motion (an oscillation). When we as humans pick up these vibrations in our ears, it gives off the sensation that we identify as pitch, or the highness or the lowness of the tone. For example, the musical note C₄ (commonly referred to as middle C), one of the most basic of musical notes that is frequently a reference point for musicians has a frequency of 261.626 Hz, thus giving it its middle-sounding pitch. Music is simply a formulated series of modulations in the pitch that is produced by an instrument resulting in a pleasant effect on the human ears. [3]

Intensity/Sensitivity



However high or low the pitch that we perceive as a single note is to our ears depends on how high or low its frequency is. If it is a faster vibrating sound wave, it sounds higher. If it vibrates lower, it sounds lower. For some it is easier to detect higher and lower frequency waves, while for others it is much harder. The range of hearing is different for different animals. The average hearing range for a young, healthy human is anywhere between 20 Hz and 20,000 Hz. As humans get older, their ability to hear higher pitched sounds starts to fade away. It is not really known why this happens, but at about the age of 20 to 25 the ability to hear sounds higher than 18,000 Hz ceases and the range continues to narrow as they get older. The hearing range for humans is different than that of other animals. For example, the hearing range for a dog is 50 Hz and as high as 45,000 Hz.
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Image courtesy of members.optushome.com.au

Now there is a difference between sensitivity and intensity. The scale for measuring the intensity of sound is called the decibel scale. The decibel scale measures the intensity of the sound waves that pass through our ears and give an easy measurement for what sounds humans can exactly stand. For example, the threshold of hearing (the lowest pitch that is present for human hearing) is at exactly 0 decibels. The threshold for pain, on the other hand, (the highest intensity of sound that can be withstood that brings pain) is 130 decibels. Intensity required for instant tympanic membrane perforation is 160 decibels. Though, in normal day-to-day interactions, a typical conversation between two people is merely 60 decibels. These are just a few examples of how the decibel scale is comprised.[4]

Behavior of Waves



In order to understand the exact properties of sound, we have to take a look at the physics and the behavior of waves of sound. As we know, sound waves are specific types of waves that are caught by the human sound receptors. The differing patterns in each unique sound wave are what give off the sensation of sound for the human brain. There are certain instances when a sound seems different to our ears in one moment than they do in another. For example, when you hear an echo of your voice or someone else's in a big room, or when certain things sound amplified in a large empty room or auditorium. These aspects of sound are crucial in the way music is constructed, performed and perfected.

Reflection/Refraction



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Image courtesy of Mt. Lebanon High School Science Department strongphysics.wikispaces.com

When sound is produced, it travels in all different directions. Some of these waves go directly to the listener’s ears (which are known as direct sound), but others fly above, away from and even below the listener. When they come across an obstacle, such as a wall or ceiling, the process known as reflection occurs, producing what is known as echoes. Reflection delays the echoes that are relative to the direct sound. The primary echoes that bounce from the closest surface between the source of the sound and the listener are called the early sound. Later reflections will become absorbed more increasingly by multiple reflections and gradually spaced closer. This collection of many late reflections is called the reverberant sound.[5]
When the word “refraction” is heard, it is usually associated with waves of light. But it also plays a key part in sound waves as well. Refraction is the bending of a wave when it enters a medium where its speed is different. As the speed of a wave changes, its direction changes as well during the refraction process. Usually refraction is referring to when a wave of light is diverted, but in this case it is referring to when a wave of sound is diverted. Sound waves do not stop when they reach the end of the medium they are travelling through or when they come across an obstacle. They simply go through a behavioral mutating process in which either they bounce off of the obstacle (in other words reflecting off of it), bend around the obstacle, or convert to travel through the obstacle or the new medium. When transferring this wave energy from the one medium to the next, part of the energy goes into reflecting that energy, and the other part goes into transmitting it. The more similar the two mediums are, the more energy goes into transmission, whereas in contrast, the more dissimilar they are, the more energy goes into reflecting it. Architects and builders of music halls and such buildings must take both reflection and refraction into consideration when deciding which materials will be best for a more pleasant sound and more efficient sound direction to the audience. Most buildings made specifically for musical performance and enjoyment are built purposefully for optimum performance accommodation knowing the physics of the way waves behave when they hit certain shapes and types of walls. [6]


Musical Instruments


Each musical instrument in each family of musical instruments has a specific structure and design that releases a distinct and unique sound wave, giving off a completely different sound. The way the waves are structured, their frequency, and the pattern at which they resound is what give individual instruments these distinctive sounds. To conceptualize this, imagine a middle C being played on a piano. Then imagine it being sung, or plucked from a guitar. The three sounds, although they may all be playing the exact same note, are astronomically different in sound quality. That is because each instrument’s structure and construction are completely different, thus rendering differing sound “textures”, if you will.

Standing Waves

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GIF courtesy of The Physics Classroom physicsclassroom.com

All instruments use a device for producing music/sound which are classified as standing waves. Standing waves are waves that remain in a constant position while oscillating. The resonant frequencies of the wave that is a result of the instrument releasing the energy correspond to standing waves with a node (or a point along a standing wave where the wave has minimal amplitude) at both ends. Ever single musical instrument utilizes standing waves to facilitate their sound wave production. Standing waves are found on everything from the strings on a violin to the bell of a trumpet.[7]

Vocal

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Image courtesy of howshealth.com

Music from human voices is produced by the vocal chords, which are located behind what is known generally as one’s “Adam’s Apple”. Energy for vocal music is supplied from the air in one’s lungs which is forced out through the vocal tract (which consists of the larynx, oral cavity, and nasal cavity) under pressure. The vocal tract is similar to a half open-end column (the pipes contained in many instruments that produce their sound), but the quality of the pitches and frequency produced by the human vocal tract is not as precise as those of such pipes, most likely due to the soft texture of the vocal tract. With the unevenness of the human vocal tract in mind, an understanding of the quality of human voice can be grasped. Pitches are created through the vibration of the vocal chords in the human throat. The frequencies at which pitches are released can be controlled by shaping the vocal tract to fit different forms and cause different vibrations to occur. The things that allow humans to control this shaping are called “articulators”. The main articulators are the lips, teeth, tongue, and the soft palette of the mouth (which is the softer area of the roof of the mouth located towards the back of the mouth that acts as the gateway between oral and nasal cavities). However, although these things allow for the vocal tract to be shaped, thus altering the frequencies at which the human voice will register, there are certain things that a singer must do in order to make those frequencies much more “musically”, which is the word used to refer to more harmoniously in vocal performance terms. These things include the larynx being lowered, the jaw being opened wider, and the tip of tongue and/or lips being pushed forward. Only then can the over-all sound be shaped to more melodious and pleasing pitches. [8]

Strings


Most string instruments (orchestral being the violin, viola, cello and bass, along with guitar and many other more casual instruments) have the structure of several strings that are pulled to a point of tension (this tension being the thing that allows the strings to produce singular notes) coupled with a hollow wooden body, which both act as resonators for the instrument. The energy for their waves comes when the strings are either plucked at or had a bow drawn across them. Although most may have the idea that the sound waves come from the vibrations in the strings, they are actually mostly produced by the vibrations in the body of the instrument. String instruments’ strings are the primary resonators of the instrument. The body of a string instrument is constructed and shaped the way it is so as to produce the desired series of musical notes; hollowed out so as to create the sound it does. [9]

Percussion


The whole percussion family of musical instruments can be summed up by the simple generalization of music being produced by something being hit. A large portion of the way percussion instruments are constructed relies fully on standing waves. When the object that creates the sound within the instrument is struck, the standing waves that vibrate through it are what radiate its sound. For example, with a piano it is the high-strength steel strings which are placed over a metal frame that are struck and create the vibrations. With a drum, it is the membrane that covers the frame of the hollow body that is struck. Percussion instruments can only create standing waves through three modes: bars and rods, membranes, and plates, all of which are struck, causing standing waves to vibrate throughout creating the desired musical response. [10]

Brass


Brass instruments give off more raspy and blaring tones than other instruments. That is because the main source of energy for the brass instrument it the player’s vibrating lips giving it air and thus creating the sound. The instrument’s player uses his or her vibrating lips to push the air through the mouthpiece and mouth pipe of the instrument. The family of brass instruments are one of the two families that are played by being blown into (the other being woodwinds). The resonant frequencies that result from the mouthpiece are preset, but through adjustments in the resonances made by the player of the air column and of his or her lips, the frequencies can be modified. The main structures of the brass family reside in two simple shapes: conical or cylindrical and are grouped together with similar instruments of that structure when being used in performance. They are paired together like this for the optimum sound wave coherence and compatibility. [11]

Woodwinds


Woodwinds, like brass instruments, get their energy from the player’s breathing. The woodwind family’s tones are much quieter than and not as forced as the brass family’s. The sound often produced by woodwinds is softer because the main resonator for the woodwinds is a reed, rather than a mouthpiece. The energy transferred into the woodwind is transmitted through the reed and out through the open-end air column and then converted into music at the frequency expressed. [12]

Conclusion


Music has been present since the beginning of time. Since the earliest people who used it as a form of communication and worship. Still to this day it is a form of free expression and inspiration for many. These are just a few of the logistics that go into creating it and what make it possible. Music is essentially the manipulation of sound waves into a purified and planned form that is enjoyable and pleasing to the auditory receptors. But to many people, it is so much more than just that. It is a way of life.









References



  1. ^ Discovery Health
  2. ^ Auditory System by Joe Steinmetz and Glen Lee
  3. ^ The Physics Classroom - Pitch and Frequency
  4. ^ The Physics Classroom - Intensity and the Decibel Scale
  5. ^ University of California - Prof. David Kirby Lecture 11 notes
  6. ^ The Physics Classroom - Reflection, Refraction, and Diffraction
  7. ^ The Physics Classroom - Resonance and Standing Wave Patterns
  8. ^ University of California - Prof. David Kirby Lecture 15 notes
  9. ^ University of California - Prof. David Kirby Lecture 11 notes
  10. ^ University of California - Prof. David Kirby Lecture 14 notes
  11. ^ University of California - Prof. David Kirby Lecture 14 notes
  12. ^ University of California - Prof. David Kirby Lecture 12 notes